#49175201

order	37504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

C₂₉₃ ⋊ #2183

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#11924078
commutator, socle, prime radical	C₂²×C₂₉₃	C₂²×C₈
Fitting	C₄⋊C₈×C₂₉₃	C₄
cosocle	C₂×#14556873	C₂³
hypercenter	C₄⋊C₈	#11924078
hypocenter	C₂₉₃	#2183
LCS	G ▷ C₂²×C₂₉₃ ▷ C₂₉₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

126 conjugacy classes of subgroups.

μ_t(G) = 37504

Polycyclic presentation:

2^7,293|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^155,h^c=h^138,h^e=h^292

1516 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37504, 20926);